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An Effective Łojasiewicz Inequality for Real Polynomials

János Kollár
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Abstract

Let H be the supremum of finitely many real polynomials of degree d and assume that H has a strict local minimum at 0. We prove a Łojasiewicz-type inequality $H(x_1,...,x_n) > ||(x_1,...,x_n)||^s$ where s depends only on d and n. This implies a similar inequality where $(x_1,...,x_n)$ runs through the points of a semi-algebraic set.

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János Kollár. 1999-04-28. An Effective Łojasiewicz Inequality for Real Polynomials. https://arxiv.org/abs/math/9904161

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